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We theoretically investigate up-conversion process of entangled two photonson a dimer molecule, which is coupled by a cavity or nanoscale metallicstructure. Within one-dimensional input-output theory, the propagators of thephotons are derived analytically and the up-conversion probability iscalculated numerically. It is shown that the coupling with the nanostructureclearly enhances the process. We also find that the enhancement becomes furtherpronounced for some balanced system parameters such as the quantum correlationbetween photons, radiation decay rates and coupling between the nanostructureand molecule. The non-monotonic dependencies are reasonably explained in viewof quantum interference between the coupled modes of the whole system. Thisresult can provide a guideline for nonlinear optical reactions by weak light ofa few photons.

Enhanced up-conversion of entangled photons and quantum interference under localized field in nanostructures